Typescript: Generics, infer the value of object if key is given

Let's say we have some kind of dispatch functions that tries to update a certain prop on an object. Is it possible to have proper type inference in the following scenario?

type EntityA = {
  name: string;
  id: number
}

type EntityB = {
  id: number;
  test1: number;
  test2: string;
  test3: number;
  test4: string;
}

type EntityAction<T> = {
  [K in keyof T]-?:
  | {
    type: 'UPDATE_ENTITY';
    payload: T;
  } |
  {
    type: 'UPDATE_PROP';
    propName: K;
    payload: T[K];
  };
}[keyof T];

function dispatch<T>(action: EntityAction<T>) {
  // omitted logic because it's not relevant
  console.log(action);
}

dispatch<EntityA>({
  type: 'UPDATE_PROP',
  propName: 'name',
});

dispatch<EntityB>({
  type: 'UPDATE_PROP',
  propName: 'test4',
  payload: ''
})

Playground here

I managed to infer the types based on a reply found here (Thanks @jcalz) but as soon as I have more than 1 prop in a type it doesn't work correctly.

Given EntityA, if i dispatch the following:

dispatch<EntityA>({ type: 'UPDATE_PROP',propName: 'id' })

it correctly lets me know that the prop payload is missing However, if I pass

dispatch<EntityA>({ type: 'UPDATE_PROP',propName: 'name' })

It tells me that Type '"name"' is not assignable to type '"id"'. (or whatever the last prop in the type is).

Any idea if this can be "fixed" to properly infer the type of payload? Is it even possible in this setup? It seems to work if EntityAction as:

export type EntityAction<T> = {
  [K in keyof T]-?:
  {
    type: 'UPDATE_PROP';
    propName: K;
    payload: T[K];
  };
}[keyof T];